Select all of the correct ordered pairs that are solutions to the following system of inequalities.
8y ≥ – 2x – 32
4x – 8y > 0
a. (0, 2)
b. (-2, -2)
c. (2, 0)
d. (4, -5)
To determine which ordered pairs are solutions to the system of inequalities, we need to substitute the x and y values in each pair into both inequalities and see if they satisfy both.
a) (0,2)
For 8y ≥ -2x - 32:
8(2) ≥ -2(0) - 32
16 ≥ -32 (True)
For 4x - 8y > 0:
4(0) - 8(2) > 0
-16 > 0 (False)
b) (-2, -2)
For 8y ≥ -2x - 32:
8(-2) ≥ -2(-2) - 32
-16 ≥ 4 - 32
-16 ≥ -28 (True)
For 4x - 8y > 0:
4(-2) - 8(-2) > 0
-8 + 16 > 0
8 > 0 (True)
c) (2,0)
For 8y ≥ -2x - 32:
8(0) ≥ -2(2) - 32
0 ≥ -4 - 32
0 ≥ -36 (True)
For 4x - 8y > 0:
4(2) - 8(0) > 0
8 > 0 (True)
d) (4, -5)
For 8y ≥ -2x - 32:
8(-5) ≥ -2(4) - 32
-40 ≥ -8 - 32
-40 ≥ -40 (True)
For 4x - 8y > 0:
4(4) - 8(-5) > 0
16 + 40 > 0
56 > 0 (True)
Therefore, the correct ordered pairs that are solutions to the system of inequalities are:
b) (-2, -2)
c) (2, 0)
d) (4, -5)